Magnetic Resonance Imaging. Pål Erik Goa Associate Professor in Medical Imaging Dept. of Physics

Transcription

1 Magnetic Resonance Imaging Pål Erik Goa Associate Professor in Medical Imaging Dept. of Physics 1

2 Why MRI? X-ray/CT: Great for bone structures and high spatial resolution Not so great for soft tissue. Ultrasound: Great for real-time imaging, quick and easily available. Not so great in terms of spatial resolution, and for imaging behind bones/air. Magnetic Resonance Imaging: Great for soft tissue, in particular brain! Not so great for bones and close to metal implants Spatial resolution ~1 mm. 2

3 MRI: Main components Requires a large magnet to put the patient in (expensive and potentially dangerous). The signal is coming from the hydrogen nucleus (proton) - > water (fat). Radio frequency antennas (coils) are used for transmitting and receiving the signal. Additional coils for generating gradients in the magnetic field needed for spatial localization/coding. Signal is acquired in Fourier-space. 3

4 4 The Magnet

5 A closer look Magnet coils: Superconducting wire at 4.2 K creating a strong magnetic field (typically T) Shim coils: Fine adjustment of magnetic field Gradient coils: Resistive wire creating linear gradients in the magnetic field used for spatial encoding RF-coils: Signal transmission and reception Individually designed for different body regions 5

6 6 Rf-coils

7 7 Operator room

8 Technical room Control electronics Cooling pump Gradient amplifiers 8

9 Rf shielding To avoid artefacts in images, the magnet-room must be shielded from all electromagnetic radiation. Walls, floor and roof is covered by copper plates. 9

10 MRI = Contrast Versatility Image contrast can be controlled and changed depending on acquisition parameters. Basic Image contrasts: Relaxation times (T1, T2, T2*) Water content (proton density) Image contrast can also be made sensitive to: Diffusion, temperature, flow, oxygen content 10

11 MR-physics: Warning MRI is based on the precession of the magnetic moment in protons (usually called spin). Is often explained using a combination of quantum physics and classical equations of motion. A simplified quantum picture is used to explain: Thermal equilibrium distribution Resonance condition Classical equations of motion are used to explain the rest. Beware that the simplified quantum picture is insufficient to describe MRI, because it does not deal with the phase of the magnetic moments. 11

12 Proton spin Atomic nuclei with odd number of nuclear particles have a physical property called spin. Since nuclei also have electric charge, the spin gives rise to a magnetic moment. The simplest atomic nucleus is the hydrogen proton. Hydrogen is everywhere in the body through water. All ordinary MRI is based on the hydrogen nucleus (proton) H + in the water molecule. S H+ N 12 All the properties described in the following relate to the proton spins.

13 Magnetic Moment H+ N Each spin is like a small compass needle: S The strength of this needle is called the magnetic moment and is determined by the gyromagnetic ratio γ. γ is a physical constant and is different for different nuclei. Proton: γ = rad/s/tesla (γ = MHz/Tesla) 13

14 Energy Levels If we put the spin in a magnetic field B 0, two possible energy states exists (quantization): 1. Up. 2. Down. More energy is needed for the Down state compared to the Up state. Energy difference involved is given by the socalled Larmor frequency ω 0 :!E = hf =!! 0 E ΔE B 0! 0 = "B 0 14

15 Resonance Whenever a spin moves between the two energy states, energy is absorbed or released: E ΔE ΔE The energy is released as an electromagnetic wave at the Larmor frequency:!e = hf 0 =!! 0 T: MHz! 0 = "B 0

16 Boltzmann distribution Gives the probability of finding an individual spin in one of the two possible energy states, given the thermal energy available: P + P! = exp ("E kt ) P + = Probability of Spin Up. P - = Probability of Spin Down. ΔE = hf. k = Boltzmanns constant ( J/K) T = Temperature (Kelvin). 16

17 Equilibrium state The Boltzmann-distribution describes the equilibrium state: If left to itself, nature will relax towards this state. Example: B 0 = 3.0 Tesla. T = 37 o Celcius. P+/P- = If you have spins, will be in the Up state, in the Down state! But: Water contains protons per ml ( ). The fraction is low, but the total number is high. 17

18 Magnetization at equilibrium The net magnetic moment from all the individual spins is called the magnetization M. Zero magnetic field: Arbitrary orientation of spins and no net magnetization. With magnetic field: A small majority of spins will align with the magnetic field and create an additional field M 0. M = 0 M M > 0 B 0 18 M 0 =! 0" 2! 2 4kT B 0

19 So far with quantum physics In the following we deal with classical equations of motion This is possible because the QM expectation value for the magnetic moment of individual spins follows the classical equations of motion. When, in the following we use the term spin, we don t necessarily mean individual spins, but larger collection of spins in a coherent state. 19

20 Precession When put in a magnetic field: Spin will rotate around the applied field Identical to the interaction between the angular moment of a spinning top and the gravitational field. Precession frequency (Larmor frequency) will depend on the applied field and the magnetic moment of the nucleus:! 0 = " B 0 20

21 Magnetization vector The magnetization vector describes the sum of all individual magnetic moments z Equilibrium: M is directed along the z- axes, magnitude given by the thermal equilibrium value (M 0 ). The precession of spins will NOT create a net rotating M in the x-y plane, due to random phases of the individual magnetic moments. B 0 M y x 21

22 Application of rf field B 0 M z In addition to the static B0, we now apply a rotating magnetic field B 1 (ω 0 ). Magnetization vector will start to precess around the total magnetic field. Results in a spiraling motion of M if viewed in the laboratory frame of reference: y x B 1 22

23 Rotating frame of reference Used to simplify the visualization of M. Rotates at the Larmor frequency. Only precession around rf-field B1 (which now appears static) is visible. 23

24 Effect of rf-field B 0 z Excitation by radio frequency radiation will bring the system away from its equilibrium state. This excitation can be described as a rotation of the magnetization vector away from the z-axis. The angle with which M rotates is called the flip angle and can be controlled (often 90 deg). rf M y' The result after the rf-pulse is a net magnetization in the x -y plane 24 M 90º x'

25 MR-signal If we jump back to the laboratory reference frame, the magnetization vector will now rotate in the x-y plane at the Larmor-frequency. This rotating magnetic field can be detected as rf-radiation -> MR signal. 25

26 MR-signal z x B 0 y time M x 26

27 Relaxation (T1) After the rf-pulse, the spin magnetization vector will relax back towards its equilibrium value, which is along the z- axis. This effect is called T1-relaxation, B 0 z longitudinal relaxation or spin-lattice relaxation. When the x-y component of M has dissappeared completely, the MR signal is lost. M y' Free Induction Decay 27 x'

28 Relaxation (T2) In most cases the x-y component of the magnetization vector disappears faster than expected from the T1-relaxation process, meaning that we loose the MRI signal faster than expected. This effect is called dephasing,t2-relaxation, transversal relaxation or spin-spin relaxation. z B 0 M y' Free induction decay 28 x'

29 Relaxation (T2) We can understand this effect by introducing phase. In phase: + = Out of phase: + = 29

30 Origin of dephasing B 0 is not identical all over the sample at all times, it varies slightly. This means rotation speed of different spins vary slightly, leading to dephasing. After a while, different spins are at different points along the circle. Eventually the spins will spread out to cover the whole circle, and the signal is lost. y x M x x 30

31 Rotating frame of reference Dephasing is better visualized in the rotating frame of reference. Here dephasing corresponds to a fanning out of the phases of the individual spins z y x 31

32 T1 versus T2 relaxation T1-relaxation: the regrowth of the z-magnetization (longitudinal magn.). Usually in the range of seconds. T2-relaxation: the loss of x y - magnetization (transverse magn.) Usually in the range of 100 ms. The two processes are usually considered independent of each other, although T2 T1. 32

33 Summary Magnetic field B 0. Resonance frequency. f =!B 0 Strength of equilibrium magnetization M 0 Magnetization vector. The net magnetic field created by all the spins. RF-pulse. Radio frequency radiation which rotates M away from z-axis. Flip Angle. Angle which the magnetization is rotated away from z-direction. FID (free induction decay). The decaying MR-signal as the system relaxes back to equilibrium. T1-relaxation. Regrowth of longitudinal magnetization. T2-relaxation. Loss of transverse magnetization. 33

34 Weighting: motivation for T1/T2 To adjust acquisition parameters to obtain different types of contrast in an MR image is called weighting. In a proton-weighted image the contrast is due to the spin density ρ 0. In a T1-weighted image the contrast is due to variation in the T1 values an so on. T1 and T2-weighted images are important because ρ 0 alone does not vary much in biological tissue. However there are big variations in T1 and T2. In addition will pathology affect T1 and T2. 34 It is important to understand how we can get T1 and T2 weighted images.

35 T1-relaxation one more time The relaxation of longitudinal magnetization is described by the Bloch-equation which simply stats: The time derivative of the z-magnetization is proportional to the distance from the equilibrium value: dm z dt = 1 T1 "# M! M 0 z $% When you solve this equation you get the following expression for the z-magnetization as a function of time t (after applying a 90º-rfpulse) M z = M 0 1! e!t T 1 "# $ % 35

36 T1-relaxation curve T1 = 1 sec M z T1 = 4 sec t (sec) 36

37 T2-relaxation The dephasing-process can similarly be described by the following Bloch-equation: dm xy dt =! 1 T 2 M xy Again we get an exponential solution (with FA = 90 o ): M xy = M 0! e "t/t 2 37

38 T2 Relaxation curve M xy T2 = 0.4 sec T2 = 0.1 sec t (sec) 38

39 39 The MR sequence An MR-experiment consists of repeated blochs of rfexcitation pulses and signal acquisition:

40 TR and TE TR = Repetition time Time between successive rf-excitation pulses. Controls T1-weighting TE = Echo Time Time between rf-excitation and signal acquisition. Controls T2-weighting 40

41 A basic signal equation S! " i$% 1 # e #TR/T 1 & 0 ' e #TE /T 2 By varying TR we control sensitivity to tissue variations in T1. By varying TE we control sensitivity to tissue variations in T2. 41

42 Short TR, short TE: T1-weighted S! " 0 i$% 1# e #TR/T 1 #TE /T 2 & ' e 42

43 T1-weighting Maximize T1-effects: Short TR Minimize T2-effects: Short TE M z M xy TR (sec) TE 43

44 Long TR, long TE: T2-weighted S! " 0 i$% 1# e #TR/T 1 #TE /T 2 & ' e 44

45 T2-weighting Minimize T1-effects: Long TR Maximize T2-effects: Long TE M z M xy TR (sec) TE 45

46 Long TR, short TE: Proton weighted S! " 0 i$% 1 # e #TR/T 1 #TE /T 2 & ' e 46

47 Proton-weighting Minimize T1-effects: Long TR Minimize T2-effects: Short TE M z M xy TR (sec) TE 47

48 There is more The signal decay due to dephasing happens through two separate processes: Dynamic dephasing (T2) Static dephasing (T2 ) The standard FID experiment is sensitive to both processes through T2*: 1 T 2 * = 1 T T 2' 48

49 Dynamic versus Static Dephasing Dynamic dephasing is the result of B 0 variations in time. Spins move around and affect each others local field. Irreversible process. All MR-sequences are sensitive to this. Static dephasing is the result of spatial BUT time constant B 0 variations. Due to imperfect magnetic field. Reversible process. FID sequence sensitive to this. The spin echo is not (next slides) 49

50 Spin-echo. In stead of measuring the FID signal it is possible to create an echo at a chosen time after the 90º excitation pulse. Is achieved by an 180º refocusing pulse Can be understood with the help of the rotating coordinate system: z 180º z Ekko 50

51 51 Spin-Echo

52 Spin echo versus FID

53 Signal acquisition The transverse magnetization vector is a complex quantity (Magnitude and phase). Both signals are aquired. Usually only the magnitude image is used. The phase image contains mostly information about B 0. 53

54 Magnitude image Phase image 54

55 So how to get an image? So far we only discussed a single MR-signal from the whole object How to spatially code the signal will be the topic of the next presentation. 55